Reducing IIR Filter Computational Workload

This document describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.

An Experimental Multichannel Pulse Code Modulation System of Toll Quality + Electron Beam Deflection Tube For Pulse Code Modulation

See this blog post for context. Pulse Code Modulation offers attractive possibilities for multiplex telephony via such media as the microwave radio relay. The various problems involved in its use have been explored in terms of a 96-channel system designed to meet the transmission requirements commonly imposed upon commercial toll circuits. Twenty-four of the 96 channels have been fully equipped in an experimental model of the system. Coding and decoding devices are described, along with other circuit details. The coder is based upon a new electron beam tube, and is characterized by speed and simplicity as well as accuracy of coding. These qualities are matched in the decoder, which employs pulse excitation of a simple reactive network.

Use Matlab Function pwelch to Find Power Spectral Density - or Do It Yourself

In this article, I'll present some examples to show how to use pwelch. You can also "do it yourself", i.e. compute spectra using the Matlab fft or other fft function. As examples, the appendix provides two demonstration mfiles; one computes the spectrum without DFT averaging, and the other computes the spectrum with DFT averaging.

Design IIR Filters Using Cascaded Biquads

This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads. We'll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix. Although we'll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc). As we'll see, the cascaded-biquad design is less sensitive to coefficient quantization than a single high-order IIR, particularly for lower cut-off frequencies.

Design IIR Bandpass Filters

In this post, I present a method to design Butterworth IIR bandpass filters. My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them. Here, we'll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m

Design IIR Butterworth Filters Using 12 Lines of Code

While there are plenty of canned functions to design Butterworth IIR filters [1], it's instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code.

Algorithms, Architectures, and Applications for Compressive Video Sensing

The design of conventional sensors is based primarily on the Shannon-Nyquist sampling theorem, which states that a signal of bandwidth W Hz is fully determined by its discrete-time samples provided the sampling rate exceeds 2W samples per second. For discrete-time signals, the Shannon-Nyquist theorem has a very simple interpretation: the number of data samples must be at least as large as the dimensionality of the signal being sampled and recovered. This important result enables signal processing in the discrete-time domain without any loss of information. However, in an increasing number of applications, the Shannon-Nyquist sampling theorem dictates an unnecessary and often prohibitively high sampling rate. (See Box 1 for a derivation of the Nyquist rate of a time-varying scene.) As a motivating example, the high resolution of the image sensor hardware in modern cameras reflects the large amount of data sensed to capture an image. A 10-megapixel camera, in effect, takes 10 million measurements of the scene. Yet, almost immediately after acquisition, redundancies in the image are exploited to compress the acquired data significantly, often at compression ratios of 100:1 for visualization and even higher for detection and classification tasks. This example suggests immense wastage in the overall design of conventional cameras.

The Art of VA Filter Design

The book covers the theoretical and practical aspects of the virtual analog filter design in the music DSP context. Only a basic amount of DSP knowledge is assumed as a prerequisite. For digital musical instrument and effect developers.

Multirate Systems and Filter Banks

During the last two decades, multirate filter banks have found various applications in many different areas, such as speech coding, scrambling, adaptive signal processing, image compression, signal and image processing applications as well as transmission of several signals through the same channel. The main idea of using multirate filter banks is the ability of the system to separate in the frequency domain the signal under consideration into two or more signals or to compose two or more different signals into a single signal.

A Review of Physical and Perceptual Feature Extraction Techniques for Speech, Music and Environmental Sounds

Endowing machines with sensing capabilities similar to those of humans is a prevalent quest in engineering and computer science. In the pursuit of making computers sense their surroundings, a huge effort has been conducted to allow machines and computers to acquire, process, analyze and understand their environment in a human-like way. Focusing on the sense of hearing, the ability of computers to sense their acoustic environment as humans do goes by the name of machine hearing. To achieve this ambitious aim, the representation of the audio signal is of paramount importance. In this paper, we present an up-to-date review of the most relevant audio feature extraction techniques developed to analyze the most usual audio signals: speech, music and environmental sounds. Besides revisiting classic approaches for completeness, we include the latest advances in the field based on new domains of analysis together with novel bio-inspired proposals. These approaches are described following a taxonomy that organizes them according to their physical or perceptual basis, being subsequently divided depending on the domain of computation (time, frequency, wavelet, image-based, cepstral, or other domains). The description of the approaches is accompanied with recent examples of their application to machine hearing related problems.

Design IIR Butterworth Filters Using 12 Lines of Code

While there are plenty of canned functions to design Butterworth IIR filters [1], it's instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code.

Digital PLL's -- Part 1

We will use Matlab to model the DPLL in the time and frequency domains (Simulink is also a good tool for modeling a DPLL in the time domain). Part 1 discusses the time domain model; the frequency domain model will be covered in Part 2. The frequency domain model will allow us to calculate the loop filter parameters to give the desired bandwidth and damping, but it is a linear model and cannot predict acquisition behavior. The time domain model can be made almost identical to the gate-level system, and as such, is able to model acquisition.

Signal Processing for Communications

The Art of VA Filter Design

The book covers the theoretical and practical aspects of the virtual analog filter design in the music DSP context. Only a basic amount of DSP knowledge is assumed as a prerequisite. For digital musical instrument and effect developers.

Fractional Delay FIR Filters

Consider the following Finite Impulse Response (FIR) coefficients:

b = [b₀ b₁ b₂ b₁ b₀]

These coefficients form a 5-tap symmetrical FIR filter having constant group delay [1,2] over 0 to f_s/2 of:

D = (ntaps - 1)/2 = 2      samples

For a symmetrical filter with an odd number of taps, the group delay is always an integer number of samples, while for one with an even number of taps, the group delay is always an integer + 0.5 samples.  Can we design a filter with arbitrary delay, say 9.3 samples?  The answer is yes -- It is possible to design a non-symmetrical FIR filter with arbitrary group delay which is approximately constant over a wide band, with approximately flat magnitude response [3,4].  Let the desired group delay be:

D = (ntaps - 1)/2 + u 

   = D₀ + u     samples,            (1)

where we call u the fractional delay and -0.5 <= u <= 0.5.  D₀ is the fixed portion of the total delay; it is determined by ntaps.  The appendix lists a simple Matlab function frac_delay_fir.m to compute FIR coefficients for a given value of u and ntaps.  The function provides coefficients with approximately flat delay and frequency responses over a frequency range approaching 0 to f_s/2.

In this post, we'll present a couple of examples using the function, then discuss the theory behind it.  Finally, we'll look at an example of a fractional delay lowpass FIR filter with arbitrary cut-off frequency.

A Simplified Matlab Function for Power Spectral Density

In an earlier post, I showed how to compute power spectral density (PSD) of a discrete-time signal using the Matlab function pwelch.  Pwelch is a useful function because it gives the correct output, and it has the option to average multiple Discrete Fourier Transforms (DFTs).  However, a typical function call has five arguments, and it can be hard to remember how to set them all and how they default.

In this post, I create a simplified PSD function by putting a wrapper on pwelch that sets some parameters and converts the output units from W/Hz to dBW/bin.  The function is named psd_simple.m, and its code is listed in the appendix.

Convolution DSP tutorial

Tutorial on convolution and basic DSP.

Introduction to Real-Time Digital Signal Processing

Chapter 1 of the book: Real-Time Digital Signal Processing: Fundamentals, Implementations and Applications, 3rd Edition

Sum of Two Equal-Frequency Sinusoids

The sum of two equal-frequency real sinusoids is itself a single real sinusoid. However, the exact equations for all the various forms of that single equivalent sinusoid are difficult to find in the signal processing literature. Here we provide those equations.

Python For Audio Signal Processing

This paper discusses the use of Python for developing audio signal processing applications. Overviews of Python language, NumPy, SciPy and Matplotlib are given, which together form a powerful platform for scientific computing. We then show how SciPy was used to create two audio programming libraries, and describe ways that Python can be integrated with the SndObj library and Pure Data, two existing environments for music composition and signal processing.